To pass or not to pass: a mathematical model for competitive interactions in rugby union

Predicting behavior has been a main challenge in human movement science. An important step within the theory of coordination dynamics is to find out the rules that govern human behavior by defining order parameters and control parameters that support mathematical models to predict the behavior of a system. Models to describe human coordination have been focused on interlimb coordination and on interpersonal coordination in affiliative tasks but not on competitive tasks. This article aims to present a formal model with two attractors to describe the interactive behavior on a 2v1 system in rugby union. Interpersonal distance and relative velocity critical values were empirically identified and were included as task constraints that define the attractor landscape. It is shown that using relative velocity as a control parameter the model offers reasonable prediction concerning the decision-making process. The model has the plasticity to adapt to other settings where interpersonal distances and relative velocities amongst system components act as significant task constraints.